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JEE Delight | B Stat/ B Math | ISI | UGB 2023 | Q4 | P&C | 51 numbers with 2023 distinct factors
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JEE Delight | B Stat/ B Math | ISI | UGB 2023 | Q4 | P&C | 51 numbers with 2023 distinct factors
Let n1, n2, . . . , n51 be distinct natural numbers each of which has exactly
2023 positive integer factors. For instance, 22022 has exactly 2023 positive
integer factors 2022 . Assume that no prime larger than
11 divides any of the ni
’s. Show that there must be some perfect cube
among the ni
’s. You may use the fact that 2023 = 7 × 17 × 17.
Support the channel:
Let n1, n2, . . . , n51 be distinct natural numbers each of which has exactly
2023 positive integer factors. For instance, 22022 has exactly 2023 positive
integer factors 2022 . Assume that no prime larger than
11 divides any of the ni
’s. Show that there must be some perfect cube
among the ni
’s. You may use the fact that 2023 = 7 × 17 × 17.
Support the channel:
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